Sunday, August 19, 2007

I seem to be having more trouble writing up posts while on vacation than I originally expected. Why I expected it to be easy to write posts on vacation is anybody's guess.

I wanted to write up a few things about Mark Wilson's masterful Wandering Significance, but I'm very slow at figuring out how to integrate it with the ideas that I think it will fit best. One aspect of the book that I found intriguing is Mark's insistence on the importance of concrete application and example. Logic and philosophy of language tend to like abstraction, but there are parts of me that much prefer the concrete as well. One of the problems with abundant abstraction that Mark points to is something that he calls the Theory T syndrome. He doesn't seem to define it anywhere that I could find but he does describe it and give some examples. It seems to be the often seen and overused move to considering only an abstract or schematized notion instead of a concrete instance. This in itself is not bad, and Mark describes many instances of abstraction, schematization, axiomatization, etc. that have proved fruitful. What the syndrome consists in is the move to schema or abstraction that excessively rarifies the notion in question. Considering only the abstractions provides too much opportunity to miss out important details or to just abstract them out. For example, when one considers an arbitrary theory T, one usually takes this on the logical model of a set of sentences closed under some form of logical consequence. This means that T is an infinite collection of sentences. One of Mark's complaints is that many things that get brought under this rubric are not fruitfully viewed as collections of sentences with that much structure. Rather, they present themselves as, in his words, intriguing proposals or guides about what to do. I think there is an example closer to home than any physical theory that he talks about. This is Russell's theory of descriptions. This theory isn't viewed as a set of sentences closed under consequence. It is, in various forms, directions about what to do when one encounters a particular string of words. There isn't a first-order theory of descriptions T that we compare to an equivalent theory T'. I think Mark puts his point entertainingly and well, so I will quote him at length (this also makes it look like I wrote more; theft 1, honest toil 0):

"While on this topic, there is a related misconception that merits deflationary comment. In rendering "theories" into schematic Ts and T's, our syndrome puffs the humble word "theory" into something quite grand, without it being exactly clear in what its grandeur consists (it reminds me of the log that was mistaken for a god in Aesop). Mild-mannered "theory," in its vernacular and scientific employments, often connotes little more than "an intriguing proposal," but it serves us well in that lowly capacity. For example, a "mean field theory" in solid state physics represents a suggestion as to how key quantities in the subject might be profitably approximated—that is, the "theory" properly qualifies as a mathematical guess that anticipates that the values of relevant physical variables will stay fairly closely to certain easy-to-calculate patterns. Such guesswork presently "belongs to physics" only because mathematicians haven’t been able to verify, by their own stricter standards of proof, that the technique actually works (a quite large portion of so-called "physical theorizing" partakes of this "mathematical guess" status). When we prattle philosophically about "theory," however, we commonly imagine that it represents some utterly freewheeling set of doctrines dreamed up by the creativity of man and is then submitted to verification or rejection at the hands of Nature. But this picture can be quite misleading. We don’t normally consider the response "about 10,000" to the question "what is 328 times 316?" qualifies as a theory, but the logical status of what are frequently called "theories" in real life physics is approximately that. To be sure, the employment of mean field averaging does represent an "intriguing proposal" and that is why we call it a "theory.""